Far from it. Meat (depending on how it is prepared) has relatively minor amounts of carbs/sugars. Proteins and fats, yes; and that's fine. Oils and fats will slow gluc absorption but that's about it. As for dairy products; again, it depends how they're prepared. Milk fine but a yog (depending on the type) will, in comparison, have more sugar. As for things like eggs, eat away lol
The media hype up lots of **** to be fair. Some jobs worth wanting to write a hard-line story. There is a thread on the forum atm that demos the silly things people some out with reg diabetes; some actually quite dangerous (e.g. for hypos give insulin; err NO NO NO)